Slant submersions from almost paracontact Riemannian manifolds

Authors

  • YILMAZ GÜNDÜZALP Department of Mathematics, Dicle University, 21280, Diyarbakır, Turkey

Keywords:

Riemannian submersion, almost paracontact Riemannian manifold, slant submersion.

Abstract

In this paper, we introduce slant submersions from almost paracontact Riemannian manifoldsonto Riemannian manifolds. We give examples and investigate the geometry of foliationswhich are arisen from the definition of a Riemannian submersion. We also find necessary andsufficient conditions for a slant submersion to be totally geodesic.

References

At. ceken, M. 2010. Semi-slant submanifolds of an almost paracontact metric manifold. Canadian

Mathematical Bulletin 53:206-217.

Baird, P. & Wood, J.C. 2003. Harmonic morphisms between Riemannian manifolds. Oxford science

publications.

Bourguignon, J.P. & Lawson, H.B. 1989. A mathematician’s visit to Kaluza- Klein theory. Rendiconti

del Seminario Matematico Università e Politecnico di Torino, Special Issue: 143-163.

Bourguignon, J.P. & Lawson, H.B. 1981. Stability and isolation phenomena for Yang-Mills fields.

Communications in Mathematical Physics 79:189-230.

Caldarella, A.V. 2010. On paraquaternionic submersions between paraquaternionic Kähler manifolds.

Acta Applicandae Mathematicae 112: 1-14.

Falcitelli, M., Ianus, S. & Pastore, A.M. 2004. Riemannian submersions and related topics. World

Scientific.

Gray, A. 1967. Pseudo-Riemannian almost product manifolds and submersions. Journal of Mathematics

and Mechanics 16:715-737.

Gündüzalp, Y. &

. S

ahin, B. 2013. Paracontact semi-Riemannian submersions. Turkish Journal of

Mathematics 37:114-128.

Gündüzalp, Y. 2013a. Slant submersions from almost product Riemannian manifolds. Turkish Journal of

Mathematics 37: 863-873.

Gündüzalp, Y. 2013b. Anti-invariant semi-Riemannian submersions from almost para-Hermitian

manifolds. Journal of Function Spaces and Applications, Volume 2013: Article ID 720623.

Ianus, S., Mazzocco, R. & Vilcu, G. E. 2008. Riemannian submersions from quaternionic manifolds.

Acta Applicandae Mathematicae 104: 83-89.

Ianus, S. & Visinescu, M. 1987. Kaluza-Klein theory with scalar fields and generalised Hopf manifolds.

Classical Quantum Gravity 4: 1317-1325.

Yilmaz Gündüzalp

Ianus, S. & Visinescu, M. 1991. Space-time compactification and Riemannian submersions, The

mathematical heritage of C.F. Gauss. World Science Publisher, River Edge, NJ, 358-371.

Ianus, S., Matsumoto, K. & Mihai, I. 1985. Almost semi-invariant submanifolds of some almost

paracontact Riemannian manifolds. Bulletin of Yamagata University 11: 121-128.

Mustafa, M.T. 2000. Applications of harmonic morphisms to gravity. Journal of Mathematical Physics

: 6918-6929.

O’Neill, B. 1996. The fundamental equations of a submersion. Michigan Mathematical Journal 13:459-

Park, K.S. 2012. H-slant submersions. Bulletin of the Korean Mathematical Society 49:329-338.

. S

ahin, B. 2011. Slant submersions from almost Hermitian manifolds. Bulletin Mathematique de la

Societe des Sciences Mathematiques de Roumanie 54(102):93-105.

Watson, B.1976. Almost Hermitian submersions. Journal of Differential Geometry 11:147-165.

Watson, B. 1983. G,G’-Riemannian submersions and nonlinear gauge field equations of general relativity,

Global analysis on manifolds. Teubner-Texte zur Mathematik, Leipzig, 57: 324-249.

Downloads

Published

04-02-2015